Proof of proveit.logic.booleans.implication.iff_intro theorem

import proveit
from proveit import defaults
from proveit import A, B
from proveit.logic import compose
from proveit.logic.booleans.implication  import iff_def
from proveit.logic.booleans.conjunction import and_if_both
from proveit.logic.equality import sub_left_side_into
theory = proveit.Theory() # the theorem's theory

%proving iff_intro

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
iff_intro:
(see dependencies)

iff_intro may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".

%qed

proveit.logic.booleans.implication.iff_intro has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.lhs_via_equality
3	instantiation	5, 6, 7	,  ⊢
	: , :
4	instantiation	8	⊢
	: , :
5	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
6	assumption		⊢
7	assumption		⊢
8	axiom		⊢
	proveit.logic.booleans.implication.iff_def